Wavelet-Based entropy measures to characterize two-dimensional fractional brownian fields

Orietta Nicolis; Jorge Mateu; Javier E. Contreras-Reyes

doi:10.3390/e22020196

Wavelet-Based entropy measures to characterize two-dimensional fractional brownian fields

Orietta Nicolis, Jorge Mateu, Javier E. Contreras-Reyes

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Renyi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes.

Original language	English
Article number	196
Journal	Entropy
Volume	22
Issue number	2
DOIs	https://doi.org/10.3390/e22020196
Publication status	Published - 1 Feb 2020

Keywords

Fractional brownian motion
Rényi entropy
Shannon entropy
Tsallis entropy
Wavelets

ASJC Scopus subject areas

General Physics and Astronomy

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10.3390/e22020196

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title = "Wavelet-Based entropy measures to characterize two-dimensional fractional brownian fields",

abstract = "The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Renyi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes.",

keywords = "Fractional brownian motion, R{\'e}nyi entropy, Shannon entropy, Tsallis entropy, Wavelets",

author = "Orietta Nicolis and Jorge Mateu and Contreras-Reyes, {Javier E.}",

note = "Funding Information: Funding: O.N. research was partially funded by the DI-03-19/R grant of the Andres Bello University (Chile), and J. M. research by Universitat Jaume I through grant UJI-B2018-04, and by Ministery of Science through grant MTM2016-78917-R. J.E.C.-R. research was partially supported by FONDECYT (Chile) grant no. 11190116. Publisher Copyright: {\textcopyright} 2020 by the authors.",

year = "2020",

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doi = "10.3390/e22020196",

language = "English",

volume = "22",

journal = "Entropy",

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T1 - Wavelet-Based entropy measures to characterize two-dimensional fractional brownian fields

AU - Nicolis, Orietta

AU - Mateu, Jorge

AU - Contreras-Reyes, Javier E.

N1 - Funding Information: Funding: O.N. research was partially funded by the DI-03-19/R grant of the Andres Bello University (Chile), and J. M. research by Universitat Jaume I through grant UJI-B2018-04, and by Ministery of Science through grant MTM2016-78917-R. J.E.C.-R. research was partially supported by FONDECYT (Chile) grant no. 11190116. Publisher Copyright: © 2020 by the authors.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Renyi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes.

AB - The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Renyi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes.

KW - Fractional brownian motion

KW - Rényi entropy

KW - Shannon entropy

KW - Tsallis entropy

KW - Wavelets

UR - http://www.scopus.com/inward/record.url?scp=85080918405&partnerID=8YFLogxK

U2 - 10.3390/e22020196

DO - 10.3390/e22020196

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AN - SCOPUS:85080918405

SN - 1099-4300

VL - 22

JO - Entropy

JF - Entropy

IS - 2

M1 - 196

ER -

Wavelet-Based entropy measures to characterize two-dimensional fractional brownian fields

Abstract

Keywords

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